Floating bodies and approximation of convex bodies by polytopes

Abstract

: We describe some results on approximation of convex bodies by polytopes. Best and random approximations are considered and compared. The geometric quantities related to the convex body, that appear naturally in such approximation questions are the affine surface areas. Those, and their relation to floating bodies, will be discussed as well. In this survey we give only a very selective collection of results on ap- proximation by polytopes.